Abstract:
The beam structure is widely used in engineering. The numerical simulation of beam structures is an important topic in computational mechanics. In this paper, the locking-free isogeometric analysis of complex three-dimensional beam structures is investigated. The technique of multiple sets of approximation functions originated from quasi-conforming finite element method is first applied to the isogeometric analysis of three-dimensional beam structures to solve the locking problem. Order-reduced approximation functions are applied to simulate the strains of beams. Global formulation of beam strains is applied, and the stiffness matrices of beam elements and patches can be combined without transformation between local and global coordinate systems. The beam structure is described by multi-patch non-uniform rational B-spline functions. The geometry is exactly described, and the geometrical error introduced by finite element mesh can be avoided. The numerical experiments prove that the proposed algorithm can effectively avoid the locking problem in Timoshenko beam formulation, and is suitable for the analysis of complex three-dimensional beam structures.